I have very dry skin which requires daily moisturizing. This also effects my scalp. Hair products I've tried don't solve the dry scalp issue. Baby oil makes my hair oily. Is there any way to moisturize my scalp without making my hair oily?

I too have very dry skin, scalp, and hair.
I wash my hair only when it needs it, usually 4 - 6 days. I used to use Dove shampoo but now use a bar of Dove soap, and I prefer it. Burt's Bees makes a bar shampoo I like too.
Strenuous activity/exercise brings out skin oils for me, including on the scalp.